What is the derivative of ln1 divided by x?

Answer 1

Given y=ln(1/x)

y'=(1/(1/x))(-x-2)=(1/(1/x))(1/x2)=x/x2=1/x

Use the chain rule. The derivative of ln(x) is 1/x. Instead of just "x" inside the natural log function, it's "1/x". Since the inside of the function is not x, the derivative must be multiplied by the derivative of the inside of the function.

So it's

1/(1/x) [the derivative of the outside function, natural log]

times

-x-2=1/x2 [the derivative of the inside of the function, 1/x]

This all simplifies to 1/x

So the derivative of ln(1/x) is 1/x